PDE methods for DWMRI Analysis and Image Registration

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PDE methods for DWMRI Analysis and Image
Registration
presented by John Melonakos NAMIC Core 1
Workshop 31/May/2007
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Outline

• Geodesic Tractography Review
• Cingulum Bundle Tractography
• ---------------------------------------------
• Fast Numerical Schemes
• Applications to Image Registration

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Contributors

• Georgia Tech-
• John Melonakos, Vandana Mohan, Allen Tannenbaum
• BWH-
• Marc Niethammer, Kate Smith, Marek Kubicki,
  Martha Shenton
• UCI-
• Jim Fallon

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Publications

• J. Melonakos, E. Pichon, S. Angenent, A.
  Tannenbaum. Finsler Active Contours. IEEE
  Transactions on Pattern Analysis and Machine
  Intelligence. (to appear 2007).
• J. Melonakos, V. Mohan, M. Niethammer, K. Smith,
  M. Kubicki, A. Tannenbaum. Finsler Tractography
  for White Matter Connectivity Analysis of the
  Cingulum Bundle. MICCAI 2007.
• V. Mohan, J. Melonakos, M. Niethammer, M.
  Kubicki, A. Tannenbaum. Finsler Level Set
  Segmentation for Imagery in Oriented Domains.
  BMVC 2007 (in submission).
• Eric Pichon and Allen Tannenbaum. Curve
  segmentation using directional information,
  relation to pattern detection. In IEEE
  International Conference on Image Processing
  (ICIP), volume 2, pages 794-797, 2005.
• Eric Pichon, Carl-Fredrik Westin, and Allen
  Tannenbaum. A Hamilton-Jacobi-Bellman approach to
  high angular resolution diffusion tractography.
  In International Conference on Medical Image
  Computing and Computer Assisted Intervention
  (MICCAI), pages 180-187, 2005.

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Directional Dependence
the new length functional
tangent direction
This is a metric on a Finsler manifold if ?
satisfies certain properties.
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Finsler Metrics

• the Finsler properties
• Regularity
• Positive homogeneity of degree one in the second
  variable
• Strong Convexity

Note Finsler geometry is a generalization of
Riemannian geometry.
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Closed CurvesThe Flow Derivation
Computing the first variation of the functional
E, the L2-optimal E-minimizing deformation is
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Open CurvesThe Value Function
Consider a seed region S½Rn, define for all
target points t2Rn the value function
curves between S and t
It satisfies the Hamilton-Jacobi-Bellman equation
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Numerics
Closed Curves
Open Curves
Level Set Techniques
Dynamic Programming (Fast Sweeping)
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Finsler vs Riemann vs Euclid
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Outline

• Geodesic Tractography Review
• Cingulum Bundle Tractography
• ---------------------------------------------
• Fast Numerical Schemes
• Applications to Image Registration

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A Novel Approach

• Use open curves to find the optimal anchor
  tract connecting two ROIs
• Initialize a level set surface evolution on the
  anchor tract to capture the entire fiber bundle.

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The Cingulum Bundle

• 5-7 mm in diameter
• ring-like belt around CC
• Involved in executive control and emotional
  processing

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The Data

• 24 datasets from BWH (Marek Kubicki)
• 12 Schizophrenics
• 12 Normal Controls
• 54 Sampling Directions

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The Algorithm Input

• Locating the bundle endpoints
• (work done by Kate Smith)

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The Algorithm Input

• How the ROIs were drawn

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Results

• Anterior View

• Posterior View

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Results
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Results
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Results A Statistical Note

• Attempt to sub-divide the tract to find FA
  significance

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Work In Progress

• Implemented a level set surface evolution to
  capture the entire bundle preliminary results.
• Working with Marek Kubicki and Jim Fallon to make
  informed subdivision of the bundle for
  statistical processing.
• Linking the technique to segmentation work in
  order to connect brain structures.

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Outline

• Geodesic Tractography Review
• Cingulum Bundle Tractography
• ---------------------------------------------
• Fast Numerical Schemes
• Applications to Image Registration

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Contributors

• Georgia Tech-
• Gallagher Pryor, Tauseef Rehman, John Melonakos,
  Allen Tannenbaum

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Publications

• T. Rehman, G. Pryor, J. Melonakos, I. Talos, A.
  Tannenbaum. Multi-resolution 3D Nonrigid
  Registration via Optimal Mass Transport. MICCAI
  2007 workshop (in submission).
• T. Rehman, G. Pryor, and A. Tannenbaum. Fast
  Optimal Mass Transport for Dynamic Active Contour
  Tracking on the GPU. In IEEE Conference on
  Decision and Control, 2007 (in submission).
• G. Pryor, T. Rehman, A. Tannenbaum. BMVC 2007 (in
  submission).

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Multigrid Numerical Schemes
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Parallel Computing
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Algorithms on the GPU
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Parallel Computing
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Parallel Computing
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Outline

• Geodesic Tractography Review
• Cingulum Bundle Tractography
• ---------------------------------------------
• Fast Numerical Schemes
• Applications to Image Registration

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The Registration Problem

• Synthetic Registration Problem

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Solution The Warped Grid

• Synthetic Registration Problem

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The Registration Problem

• Before

• After

• Brain Sag Registration Problem

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Solution The Warped Grid
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Speedup
A 1283 registration in less than 15 seconds
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Key Conclusions

• Multigrid algorithms on the GPU can dramatically
  increase performance
• We used Optimal Mass Transport for registration,
  but other PDEs may also be implemented in this way

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Questions?